Question

How do you solve ${p^2} - 4p + 4 = 0$ using the quadratic formula?

Answer 1

Hint: To solve this problem we should know about quadratic equations and quadratic formulas.
Quadratic equation: It is any equation that can be rearranged in standard form as $a{x^2} + bx + c = 0$ where $x$ is represent a unknown and $a,b\,and\,c$ represent known number, where $a \ne 0$ if $a = 0$ then it will change into a linear equation.
Quadratic formula: The formula that is used to calculate the solution of a quadratic equation.
Let quadratic equation is $a{x^2} + bx + c = 0$ then its solution will be,
 $x = \dfrac{{ - b \pm \sqrt {{b^2} - 4ac} }}{{2a}}$

Complete step by step solution:
As given in question ${p^2} - 4p + 4 = 0$ .
Compare it with $a{x^2} + bx + c = 0$ to calculate the value of $a,b\,and\,c$ .
We get, $a = 1,b = - 4\,and\,c = 4$
As we know, the quadratic formula is used to find the roots of a quadratic equation.
So, keeping value in the quadratic equation. We get,
 ${x_{1,2}} = \dfrac{{ - b \pm \sqrt {{b^2} - 4ac} }}{{2a}}$
 $ \Rightarrow {x_{1,2}} = \dfrac{{ - ( - 4) \pm \sqrt {{{( - 4)}^2} - 4.1.4} }}{{2.1}}$
By further solving it. We get,
 $ \Rightarrow {x_{1,2}} = \dfrac{{4 \pm \sqrt {16 - 16} }}{2} = \dfrac{4}{2} = 2$
From the above calculation. We get
The roots of the quadratic equation will be the same, that is $x = 2$ .

Note: We can also do this quadratic equation by factorization by grouping which is also a suitable and easiest method. The quadratic equation is used in our daily life like applied physics, engineering and research and development. When we throw a ball its motion is parabolic whose path will be calculated by using a quadratic equation. So, so much machinery in defense is based on it.